Question

A.

Answer 1

Answer:

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

b. The y intercept is 11

c. The x intercept is $-\frac{11}{4}$

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

e. See attachment for graph

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

$x = -\frac{11}{4}$

The x intercept is $-\frac{11}{4}$

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