Question

Grafics (4,-7); 2x-7y=9

the equation of the line is y=

Answer 1

The equation is 2x - 7y = 9.

The slope intercept form of a line is y = mx + b.

the original equation is 2x - 7y = 9.

Add 7y to each side.

2x = 9 + 7y

9 + 7y = 2x

Subtract 9 from each side.

7y = 2x - 9

Divide each side by 7.

y = (2/7)x - 9/7.

Compare the above equation with slope intercept form y = mx + b.

Slope m = 2/7.

Say the point  (x1, y1)=(4, -7)

The line is y - y1 = m(x - x1).

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

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

y  =2/7(x - 4) - 7

y  = (2x - 8 - 49) /7

y  = (2/7)x - 57/7.

The line is y = (2/7)x - 57/7.

Compare the above equation with slope intercept form y = mx + b.

Slope m = 2/7 and y - intercept is -57/7.

y-intercept is -57/7,so the line crosses the y-axis at (0, -57/7).

Using slope find the next point.

Slope = rise/run = 2/7.

Start at point (0, -57/7),move 2 units up and 7 units right,then plot the point(14, -4).

draw a line through these points.

Graph :