Question

2. Write the slope-intercept form of the equation of the line through the given point with the given slope.

through: (-2,-5), slope = 4

show your work

Answer 1

`\boxed{\bf{y=4x+3}}`

Explanation:

We are given the following information:

• the line passes through (-2,-5)
• the line has a slope of 4

Use the point-slope formula:

`\bf{y-y_1=m(x-x_1)}`

Substitute the values.

`\bf{y-(-5)=4(x-(-2)}`

simplify:

`\bf{y+5=4(x+2)}`

use the distributive property to disttribute 4.

`\bf{y+5=4x+8}`

subtract 5 from both sides:

`\bf{y=4x+8-5}`

simplify!

`\boxed{\bf{y=4x+3}}`

Answer 2

y = 4x + 3

Explanation:

Slope intercept form: y = mx + b

Given: Point (-2, -5), Slope (m) = 4

1. Substitute the slope intercept form with your given variables:

New equation: -5 = (4 x -2) + b

2. Simplify the right side

New Equation: -5 = -8 + b

3. Isolate b by adding 8 on both sides of the equation.

New equation: b = 3

Now, we know that b (y-intercept) = 3

4. Rewrite your equation:

New equation (final answer): y = 4x + 3