Question

Write an equation in point slope form of the line that passes through the point (-4, 5) and has a slope of 3/8

Answer 1

Our answer is y = 3/8x + 6.5

`\Large\texttt{Explanation}`

We are asked to write the equation for a line that passes through (-4,5) and has a slope of 3/8.

So, we will use our point-slope formula:

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

↬ Substitute the values:

`\blacktriangleright\quad\bf{y-5=\cfrac{3}{8}(x-(-4)}`

`\blacktriangleright\quad\bf{y-5=\cfrac{3}{8}(x+4)}` <= point-slope equation

↬ Distribute 3/8:

`\blacktriangleright\quad\bf{y-5=\cfrac{3}{8}x+1.5}`

↬ Add 5 to both sides:

`\blacktriangleright\quad\bf{y=\cfrac{3}{8}x+1.5+5}`

`\blacktriangleright\quad\boxed{\bf{y=\cfrac{3}{8}x+6.5}}`

↬
`\therefore` Our answer is y = 3/8x + 6.5.

Answer 2

`y - 5 = \ (3)/(8) (x + 4)`