Question

A.

2. A line with a slope of 4 passes through the point (-2, 3).
Write the equation for this line in slope-interceptform
b. Identify the y-intercept.
Identify the x-intercept.
Convert the equation to standard form.
Sketch a graph representing this line.
C.
d.
e.
ning through then​

Answer 1

a. Slope intercept form:
`y= 4x +11`

b. The y intercept is 11

c. The x intercept is
`-(11)/(4)`

d. Standard Form:
`y - 4x = 11`

e. See attachment for graph

Step-by-step explanation:

Given

Slope (m)

`m = 4`

`(x_1,y_1) = (-2,3)`

Solving (a): The line equation in slope intercept

This is solved using:

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

Substitute values for y1, x1 and m

`y - 3 = 4(x - (-2))`

`y - 3 = 4(x +2)`

`y - 3 = 4x +8`

Add 3 to both sides

`y - 3 +3= 4x +8 + 3`

`y= 4x +11`

Solving (b): The y intercept

To do this, we simply take x as 0.

Substitute 0 for x in
`y= 4x +11`

`y = 4(0) + 11`

`y = 0 + 11`

`y = 11`

The y intercept is 11

Solving (c): The x intercept

To do this, we simply take y as 0.

Substitute 0 for y in
`y= 4x +11`

`0 = 4x + 11`

Collect Like Terms

`4x=0-11`

`4x=-11`

Solve for x

`x = -(11)/(4)`

The x intercept is
`-(11)/(4)`

The y intercept is 11

d. The equation in standard form

Equation in standard form is written in the following format:
`Ax + By = c`

`y= 4x +11`

Subtract 4x from both sides

`y - 4x = 4x - 4x + 11`

`y - 4x = 11`

Hence, the equation in standard form is
`y - 4x = 11`

e. The graph

We have that:

`(-2,3)` ---- given

In (b), we calculated the y intercept to be 11.

This implies that:
`(0,11)`

So, we can plot the graph through
`(0,11)` and
`(-2,3)`

See attachment for graph