Question

** HELP ASAP!! **write an equation in slope intercept form of the line that has a slope = -3/2, and passes through the point (-3, 3)

Answer 1

Given :-

• Slope of the line is -3/2 .
• It passes through (-3,3) .

To Find :-

• The equation of the line .

Solution :-

Here it's given that ,

$\longrightarrow m =\dfrac{-3}{2}$

And a point that is (-3,3) . We can use the point slope form of the line which is ,

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

Substituting the respective values,

$\longrightarrow y - 3 = \dfrac{-3}{2}\{ x -(-3)\}$

Simplify,

$\longrightarrow y -3 = \dfrac{-3}{2}( x +3)$

Simplify by opening the brackets ,

$\longrightarrow y - 3 =\dfrac{-3}{2}x -\dfrac{9}{2}$

Add 3 on both sides ,

$\longrightarrow y = \dfrac{-3}{2}x -\dfrac{9}{2}+3$

Add ,

$\longrightarrow \underline{\underline{ y =\dfrac{-3}{2}x -\dfrac{3}{2}}}$

This is the required answer in slope intercept form .

Answer 2

Based on given conditions,

$m = - \frac{3}{2}$

Substitute,

$m = - \frac{3}{2} \\ x = - 3 \: \: \: into \\ y = 3$

So,

$y = mx + b$

$= > 3 = - \frac{3}{2} \times ( - 3) + b$

As signs are both minus, write,

$3 = \frac{3 \times 3}{2} + b$

$= > 3 = \frac{9}{2} + b$

Rearranging equations,

$= > - b = \frac{9}{2} - 3$

Findind LCM as 2,

$= > - b = \frac{9}{2} \times \frac{3 \times 2}{1 \times 2}$

$= > - b = \frac{9 - 6}{2}$

$= > - b = \frac{3}{2}$

$= > b = - \frac{3}{2}$

Now substitute,

$m = - \frac{ 3}{2} \: \: \: into \\ b = - \frac{3}{2}$

So,

$y = mx + b$

$= > y = - \frac{3}{2} \times x + \frac{ - 3}{2}$

Rewriting in slope intercept form:

(Please check attached image)