Graph the lines containing these points and find their slope.

Question

(4,-7) (2,3).

Answer 1

The points are (4, - 7) and (2, 3).

Slope - intercept form : y = mx + b.

Line equation formula : y - y₁ = m(x - x₁).

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Substitute the values of (x₁, y₁) = (4, - 7) and (x₂, y₂) = (2, 3) in (m) = (y₂ - y₁)/(x₂ - x₁).

= (3 + 7)/(2 - 4)

= (10)/(- 2)

m = - 5.

Substitute the values of (x₁, y₁) = (4, - 7) and m = - 5 in Line equation formula.

y + 7  = - 5(x - 4)

y = - 5(x) + 20 - 7

y = - 5x + 13.

The slope - intercept form of the line is y = - 5x + 13.

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

slope = - 5 and y-intercept is 13.

y-intercept is 13, so the line crosses the y-axis at (0, 13)

Using slope find the next point.

Slope = rise/run = -5/1

Start at point (0, 13), move 5 units down and 1 unit right, then plot the point (1, 8).

Draw a line through these points.

Graph :