Question

Use point-slope form to write the equation of a line that passes through the point (-13,-19) with the slope 7/6

Answer 1

To find the equation of a line using point-slope form that passes through (-13, -19) with a slope of 7/6, you plug these values into the formula and simplify to get y + 19 = (7/6)(x + 13).

Step-by-step explanation:

The question asks to write the equation of a line using point-slope form, which is y - y1 = m(x - x1), where m is the slope and (x1, y1) is the point the line passes through.

To write the equation for a line that passes through the point (-13, -19) with a slope of 7/6, we plug these values into the point-slope form:

`\[y - (-19) = (7)/(6)(x - (-13))\]`

Simplifying this, we get:

`\[y + 19 = (7)/(6)(x + 13)\]`

This is the equation of the line in point-slope form.

Answer 2

Answer:
`y = (7)/(6)x - (23)/(6)`

Work Shown:

`y - y_1 = m(x - x_1)\\\\y - (-19) = (7)/(6)(x - (-13))\\\\y + 19 = (7)/(6)(x + 13)\\\\y + 19 = (7)/(6)x + (7)/(6)*13\\\\y + 19 = (7)/(6)x + (91)/(6)\\\\y = (7)/(6)x + (91)/(6) - 19\\\\y = (7)/(6)x + (91)/(6) - 19*(6)/(6)\\\\y = (7)/(6)x + (91)/(6) - (114)/(6)\\\\y = (7)/(6)x + (91-114)/(6)\\\\y = (7)/(6)x - (23)/(6)\\\\`