Question

Write in slope-intercept form of the equation of the line described. through: (-3. -2), parallel to \large y=\frac{4}{7}x-3 a \large y=\frac{5}{7}x-\frac{2}{7} b \large y=\frac{4}{7}x-\frac{2}{7} c \large y=-\frac{4}{7}x-\frac{2}{7} d \large y=\frac{5}{7}x-\frac{2}{7}

Answer 1

`y=(4)/(7) x-(2)/(7)`

Step-by-step explanation:

The equation of a straight line is given by:

y = mx + b;

where y, x are variables, m is the slope of the line and b is the y intercept.

If two lines are parallel to each other, then they have the same slope, i.e. their slopes are equal.

The equation of a line passing through the point (-3, -2) and parallel to the line y = (4/7)x - 3, would have the same slope as the line y = (4/7)x - 3

The slope (m) of the line y = (4/7)x - 3 is 4/7, hence the line passes through the point (-3, -2) with a slope of 4/7.

The equation of the line is given by:

`y-y_1=m(x-x_1)\\\\y-(-2)=(4)/(7)(x-(-3)) \\\\y + 2=(4)/(7) (x+3)\\\\y=(4)/(7)x+(12)/(7)-2\\\\y=(4)/(7) x-(2)/(7)`