Question

Choose the equation below that represents the line passing through the point (−5, 1) with a slope of three halves.
A y − 5 = three halves(x + 1)
B y + 1 = three halves(x − 5)
C y + 5 = three halves(x − 1)
D y − 1 = three halves(x + 5)

Answer 1

$\bf \begin{array}{lllll} &x_1&y_1\\ % (a,b) &({{ -5}}\quad ,&{{ 1}})\quad % (c,d) \end{array} \\\\\\ % slope = m slope = {{ m}}= \cfrac{rise}{run} \implies\cfrac{3}{2} \\\\\\ % point-slope intercept y-{{ y_1}}={{ m}}(x-{{ x_1}})\implies y-1=\cfrac{3}{2}(x-(-5))\\ \\ \left. \qquad \right. \uparrow\\ \textit{point-slope form} \\\\\\ y-1=\cfrac{3}{2}(x+5)$

Answer 2

Answer: The correct option is D, i.e., y − 1 = three halves(x + 5).

Explanation:

It is given that the line passing through the point (−5, 1) with a slope of three halves.

The equation of line passing through the point $(x_1,y_1)$ with slope m is defined as,

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

It is a point slope form.

Since we have point (-5,1) and slope three halves. Put these value in the above point slope form.

$y-1=\text{three halves}(x-(-5))$

$y-1=\text{three halves}(x+5)$

This equation is same as equation is shown in option D, therefore the option D is correct.