Question

find the equation (in slope-intercept form) of the line with the given slope that passes through the point with the given coordinates.

slope: \\(\frac{3}{2}\\), ordered pair: \\((-5, 4)\\)

Explanation:

Identify the given values

Using the Slope of a Line knowledge point

$$
LATEXBLOCK0
$$

Apply the point-slope formula

We use the point-slope equation of a line:

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

Substituting the given values:

$$ y - 4 = \frac{3}{2}(x - (-5)) $$

$$ y - 4 = \frac{3}{2}(x + 5) $$

Distribute the slope

We distribute the fraction across the terms in the parentheses:

$$ y - 4 = \frac{3}{2}x + \frac{15}{2} $$

Solve for y to find slope-intercept form

Using the Slope-Intercept Form knowledge point

$$
LATEXBLOCK1
$$

Answer:

Find the equation (in slope-intercept form) of the line with the given slope that passes through the point with the given coordinates.

slope: \(\frac{3}{2}\), ordered pair: \((-5, 4)\)

<blank>\(y = \frac{3}{2}x + \frac{23}{2}\)</blank>