Question

Write an equation in slope-intercept form of a line passing through the given point andparallel to the given line.12. (-1,2); y=3x+ 113. (4, 2); x+ y= 114. (0,-4);2x+y=315. (5, -3); 4x + 5y = 10

Answer 1

12. y = 3x + 5

Step-by-step explanation:

Two lines are parallel if they have the same slope.

In an equation of the form y = 3x + 1, the equation is the number beside the x, so the slope is 3. Then our line will have a slope of 3 and pass through the point (-1, 2).

The equation of a line with slope m that passes through the point (x1, y1) is

`y-y_1=m(x-x_1)`

Replacing m = 3 and (x1, y1) = (-1, 2), we get:

`\begin{gathered} y-2=3(x-(-1_{})) \\ y-2=3(x+1) \end{gathered}`

To write in slope-intercept form, we need to solve the equation for y, so

`\begin{gathered} y-2=3(x)+3(1) \\ y-2=3x+3 \\ y-2+2=3x+3+2 \\ y=3x+5 \end{gathered}`

So, the answer for question 12 is y = 3x + 5