Find slope and Y intercept of (4,6) and (-1,2)

Question

Need to find the slope and Y intercept of these two points and how would I graph this once I find the slop and Y intercept?

Answer 1

The points are (4, 6) and (- 1, 2).

Slope - intercept - form of a line equation is y = mx + c, where, m is slope and c is y - intercept.

Slope (m ) = (y ₂ - y ₁)/(x ₂ -x ₁).

Substitute the values of (x ₁, y ₁) = (4, 6) and (x ₂, y ₂) = (- 1, 2) in m = (y ₂ - y ₁)/(x ₂ -x ₁).

m = (2 -  6) / (- 1 - 4)

m = - 4 /(- 5)

⇒ Slope (m ) = 4/5.

Substitute the values of m = 4/5 and (x, y ) = (4, 6) in slope - intercept - form of a line equation : y = mx + c.

6 = (4/5)(4) + c

6 = 16/5 + c

c = 6 - 16/5 = ( 3 0 - 16)/5

⇒ y - intercept (c ) = 14/5.

Substitute the values of m =4/5 and c = 14/5 in slope - intercept - form of a line equation : y = mx + c.

y = (4/5)x + 14/5.

Therefore, slope - intercept - form of a line equation through the given points is y = (4/5)x + (14/5).

Since, the y - intercept is 14/5, the line crosses the y - axis at (0, 14/5).

Using slope find the next point.

Slope = rise/run = 4/5

Start at point (0,  14/5), move 4 units up and 5 units right, then plot the point (5, 34/5).

Draw a line through these points.