Question

Write an equation in slope intercept form of the line that passes through the given point and parallel to the given line. (-3,5); y=3/4x-4 ASAP PLS HELP

Answer 1

Explanation:

Since the lines are parallel, they got equal slopes

m1 = m2

First, what's the slope of the first line y = ¾x - 4

y = ¾x - 4 compared to y = mx + c

yh, m = ¾ [I hope u understand that... That's coefficient]

m1 = ¾

Then, m1 = m2 = ¾ [parallel lines]

Yh, we use:

y - y1 = m(x - x1)

y - 5 = ¾( x - (-3) )

4(y - 5) = 3(x + 3)

4y - 20 = 3x + 9

4y = 3x + 29

y = ¾x + 29/4

The equation is y = ¾x + 29/4

Answer 2

`y=(3)/(4)x+(29)/(4)`

Explanation:

The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.

Given line:

`y=(3)/(4)x-4`

The given line is in slope-intercept form. Therefore:

• slope = 3/4
• y-intercept = -4

The slopes of parallel lines are the same.

Therefore, the slope of a line parallel to the given line is also 3/4.

Given the parallel line passes through the point (-3, 5), substitute this and the found slope into the slope-intercept formula and solve for b:

`\implies y=mx+b`

`\implies 5=(3)/(4)(-3)+b`

`\implies 5=-(9)/(4)+b`

`\implies 5+(9)/(4)=-(9)/(4)+b+(9)/(4)`

`\implies b=5+(9)/(4)`

`\implies b=(20)/(4)+(9)/(4)`

`\implies b=(20+9)/(4)`

`\implies b=(29)/(4)`

Therefore, the equation of the line that passes through the given point and is parallel to the given line in slope-intercept form is:

`y=(3)/(4)x+(29)/(4)`