MATH SOLVE

6 months ago

Q:
# 1. Write the equation in slope-intercept form. Identify the slope and y-intercept. SHOW ALL WORK 2x - 3y = 92. Write the equation in slope-intercept form. Identify the slope and y-intercept. SHOW ALL WORKx - 4y = -203. Find the x- and y-intercepts for -x + 4y = 12. Write each intercept as a unique ordered pair. SHOW ALL WORK4. y = 2/3x + 7 written in standard form using integers is 3x - y = 21.A) TrueB) False5. Write an equation of a line that has the same slope as 2x – 5y = 12 and the same y-intercept as 4y + 24 = 5x.A) y= 2/5x−6B) y=6x−2/5C) y=5/2x−6 D) y=1/6x−5/26. Write the equation of a line that is perpendicular to the given line and that passes through the given point.x + 8y = 27; (–5, 5)A) y=-1/8x-45B) Y=1/8x+45C) y=8x+45D) y=-8x+457. Are the graphs of the lines in the pair parallel? Explain.y = 8/3x+ 198x – 3y = 17A) Yes, since the slopes are the same and the y-intercepts are different.B) No, since the y-intercepts are different.C) Yes, since the slopes are the same and the y-intercepts are the same.D) No, since the slopes are different.8. A line passes through (2, –1) and (8, 4).a. Write an equation for the line in point-slope form. (2 points)b. Rewrite the equation in standard form using integers. (2 points)SHOW ALL WORK9. Write at least one complete sentence with a capital letter and punctuation describing slope and how to find it.10. Find the slope of the line passing through the points (-3, -1) and (-1, 5). SHOW ALL WORK11. Write an equation in point-slope form for the line through the given point with the given slope.(10, –9); m = - 2A) y - 10 = -2(x + 9)B) y - 9 = -2(x - 10)C) y - 9 = -2(x + 10)D) y + 9 = -2(x - 10)

Accepted Solution

A:

Part 1)we know thatthe equation of the line in slope-intercept form is equal to[tex]y=mx+b[/tex]wherem is the slopeb is the y-interceptwe have[tex]2x-3y=9[/tex]solve for y[tex]3y=2x-9[/tex][tex]y=(2/3)x-3[/tex] -------> equation of the line in slope-intercept formsothe slope m is [tex]\frac{2}{3}[/tex]the y-intercept b is [tex]-3[/tex]Part 2)we know thatthe equation of the line in slope-intercept form is equal to[tex]y=mx+b[/tex]wherem is the slopeb is the y-interceptwe have[tex]x-4y=-20[/tex]solve for y[tex]4y=x+20[/tex][tex]y=(1/4)x+5[/tex] -------> equation of the line in slope-intercept formsothe slope m is [tex]\frac{1}{4}[/tex]the y-intercept b is [tex]5[/tex]Part 3)we know thatThe x-intercept is the value of x when the value of y is equal to zeroThe y-intercept is the value of y when the value of x is equal to zerowe have[tex]-x+4y=12[/tex]a) Find the x-interceptFor [tex]y=0[/tex] substitute in the equation[tex]-x+4*0=12[/tex][tex]x=-12[/tex]The answer part 3a) is [tex](-12,0)[/tex]b) Find the y-interceptFor [tex]x=0[/tex] substitute in the equation[tex]-0+4y=12[/tex][tex]y=3[/tex]The answer part 3b) is [tex](0,3)[/tex]Part 4)we know thatthe equation of the line in standard form is[tex]Ax+By=C[/tex] we have[tex]y=\frac{2}{3}x+7[/tex]Multiply by [tex]3[/tex] both sides[tex]3y=2x+21[/tex][tex]2x-3y=-21[/tex] ------> equation in standard formthereforethe answer Part 4) is option B FalsePart 5)Step 1Find the slopewe have[tex]2x-5y=12[/tex]solve for y[tex]5y=2x-12[/tex][tex]y=(2/5)x-(12/5)[/tex]sothe slope m is [tex]\frac{2}{5}[/tex]Step 2Find the y-interceptThe y-intercept is the value of y when the value of x is equal to zerowe have[tex]4y+24=5x[/tex]for [tex]x=0[/tex][tex]4y+24=5*0[/tex][tex]4y=-24[/tex][tex]y=-6[/tex]the y-intercept is [tex]-6[/tex]Step 3Find the equation of the linewe have[tex]m=\frac{2}{5}[/tex][tex]b=-6[/tex]the equation of the line in slope-intercept form is [tex]y=mx+b[/tex]substitute the values[tex]y=\frac{2}{5}x-6[/tex]thereforethe answer Part 5) is the option A [tex]y=\frac{2}{5}x-6[/tex]Part 6) Step 1Find the slope of the given linewe know thatif two lines are perpendicular. then the product of their slopes is equal to minus oneso[tex]m1*m2=-1[/tex]in this problem the given line[tex]x+8y=27[/tex]solve for y[tex]8y=27-x[/tex][tex]y=(27/8)-(x/8)[/tex]the slope m1 is [tex]m1=-\frac{1}{8}[/tex]sothe slope m2 is [tex]m2=8[/tex]Step 2Find the equation of the linewe know thatthe equation of the line in slope point form is equal to[tex]y-y1=m*(x-x1)[/tex]we have[tex]m2=8[/tex]point [tex](-5,5)[/tex]substitutes the values[tex]y-5=8*(x+5)[/tex][tex]y=8x+40+5[/tex][tex]y=8x+45[/tex]thereforethe answer part 6) is the option C [tex]y=8x+45[/tex]Part 7)[tex]y=(8/3)x+ 19[/tex] -------> the slope is [tex]m=(8/3)[/tex]

[tex]8x- y=17[/tex][tex]y =8x-17[/tex] --------> the slope is [tex]m=8[/tex]we know thatif two lines are parallel , then their slopes are the samein this problem the slopes are not the sametherefore the answer part 7) is the option D) No, since the slopes are different.Part 8)a. Write an equation for the line in point-slope formb. Rewrite the equation in standard form using integersStep 1Find the slope of the linewe know thatthe slope between two points is equal to[tex]m=\frac{(y2-y1)}{(x2-x1)}[/tex]substitute the values[tex]m=\frac{(4+1)}{(8-2)}[/tex][tex]m=\frac{(5)}{(6)}[/tex] Step 2Find the equation in point slope formwe know thatthe equation of the line in slope point form is equal to[tex]y-y1=m*(x-x1)[/tex]we have[tex]m=(5/6)[/tex]point [tex](2,-1)[/tex]substitutes the values[tex]y+1=(5/6)*(x-2)[/tex] -------> equation of the line in point slope formStep 3Rewrite the equation in standard form using integers[tex]y=(5/6)x-(5/3)-1[/tex][tex]y=(5/6)x-(8/3)[/tex]Multiply by [tex]6[/tex] both sides[tex]6y=5x-16[/tex][tex]5x-6y=16[/tex] --------> equation of the line in standard formPart 9)we know thatThe formula to calculate the slope between two points is equal to[tex]m=\frac{(y2-y1)}{(x2-x1)}[/tex]where(x1,y1) ------> is the first point(x2,y2) -----> is the second pointIn the numerator calculate the difference of the y-coordinatesin the denominator calculate the difference of the x-coordinatesPart 10)we know thatThe formula to calculate the slope between two points is equal to[tex]m=\frac{(y2-y1)}{(x2-x1)}[/tex]substitutes[tex]m=\frac{(5+1)}{(-1+3)}[/tex][tex]m=\frac{(6)}{(2)}[/tex][tex]m=3[/tex]thereforethe answer Part 10) is [tex]m=3[/tex]Part 11)we know thatthe equation of the line in slope point form is equal to[tex]y-y1=m*(x-x1)[/tex]substitute the values[tex]y+9=-2*(x-10)[/tex] --------> this is the equation in the point slope form

[tex]8x- y=17[/tex][tex]y =8x-17[/tex] --------> the slope is [tex]m=8[/tex]we know thatif two lines are parallel , then their slopes are the samein this problem the slopes are not the sametherefore the answer part 7) is the option D) No, since the slopes are different.Part 8)a. Write an equation for the line in point-slope formb. Rewrite the equation in standard form using integersStep 1Find the slope of the linewe know thatthe slope between two points is equal to[tex]m=\frac{(y2-y1)}{(x2-x1)}[/tex]substitute the values[tex]m=\frac{(4+1)}{(8-2)}[/tex][tex]m=\frac{(5)}{(6)}[/tex] Step 2Find the equation in point slope formwe know thatthe equation of the line in slope point form is equal to[tex]y-y1=m*(x-x1)[/tex]we have[tex]m=(5/6)[/tex]point [tex](2,-1)[/tex]substitutes the values[tex]y+1=(5/6)*(x-2)[/tex] -------> equation of the line in point slope formStep 3Rewrite the equation in standard form using integers[tex]y=(5/6)x-(5/3)-1[/tex][tex]y=(5/6)x-(8/3)[/tex]Multiply by [tex]6[/tex] both sides[tex]6y=5x-16[/tex][tex]5x-6y=16[/tex] --------> equation of the line in standard formPart 9)we know thatThe formula to calculate the slope between two points is equal to[tex]m=\frac{(y2-y1)}{(x2-x1)}[/tex]where(x1,y1) ------> is the first point(x2,y2) -----> is the second pointIn the numerator calculate the difference of the y-coordinatesin the denominator calculate the difference of the x-coordinatesPart 10)we know thatThe formula to calculate the slope between two points is equal to[tex]m=\frac{(y2-y1)}{(x2-x1)}[/tex]substitutes[tex]m=\frac{(5+1)}{(-1+3)}[/tex][tex]m=\frac{(6)}{(2)}[/tex][tex]m=3[/tex]thereforethe answer Part 10) is [tex]m=3[/tex]Part 11)we know thatthe equation of the line in slope point form is equal to[tex]y-y1=m*(x-x1)[/tex]substitute the values[tex]y+9=-2*(x-10)[/tex] --------> this is the equation in the point slope form