Question

Write the equation in standard form (ax + by = c) using only integers for the line described. Passing through (-4, 2) and parallel to y = -3/2x +1

Answer 1

Step-by-step explanation:

The point-slope form of an equation is given by

`y-y_0=m(x-x_0)`

where (x0, y0) is a point on the line and m is the slope.

A line that is parallel to y = -3/2 x +1 has the same slope, namely -3/2; therefore, we know that our equation must look like

`y-y_0=-(3)/(2)(x-x_0)`

where (y0, x0) is a point hitherto unknown.

Furthermore, we also know that the line passes through the point (-4, 2) and therefore, we set (x0, y0) = (-4, 2) - this gives

`y-2=-(3)/(2)(x+2)`

which is our equation in point-slope form. However, we are asked to convert it into the standard form.

Expanding out the right-hand side gives

`y-2=-(3)/(2)x-3`

adding 3/2 x to both sides gives

`y+(3)/(2)x-2=-3`

Finally, adding 2 to both sides gives

`y+(3)/(2)x=-3+2`
`y+(3)/(2)x=-1`

which is our answer!