Use point-slope form to write the equation of a line that passes through the point (-13,-12) with slope 19/12

Answer 1

The point-slope form of a linear equation is given by:

y - y1 = m(x - x1)

Where (x1, y1) is a point on the line and m is the slope.

Given the point (-13,-12) and slope 19/12, we can write the equation in point-slope form as:

y - (-12) = (19/12)(x - (-13))

Simplifying:

y + 12 = (19/12)(x + 13)

At this point, we can multiply both sides of the equation by 12 to eliminate the fraction:

12(y + 12) = 12(19/12)(x + 13)

12y + 144 = 19(x + 13)

Now we can distribute the 19 through the parenthesis on the right side:

12y + 144 = 19x + 247

Finally, we can rearrange the equation to have the form y = mx + b, which is slope-intercept form:

12y = 19x + 247 - 144

12y = 19x + 103

Divide both sides of the equation by 12 to isolate y:

y = (19/12)x + (103/12)

Therefore, the equation of the line that passes through the point (-13,-12) with slope 19/12 is y = (19/12)x + (103/12).