Slope and Right Triangles

Find the equation of this line.

• y = 1.5x + 2

• y = 2x + 2

• y = 2.5x + 2

• y = 3x + 2

Answer explanation

The y-intercept is 2. The slope is the tangent of the angle: tan(56.31) = 1.5. So the equation is

y = 1.5x + 2.

FInd the equation of a line that has a y-intercept of 2 and makes a 51.34° angle with the y-axis.

• y = 0.6x + 2

• y = 0.7x + 2

• y = 0.8x + 2

• y = 0.9x + 2

Answer explanation

The angle inside the slope triangle would be

90-51.34 degrees. So the slope of the line is

tan(38.66) = 0.8.

What is the length of y in this picture?

• 45

• 5√2

• 90

• 5

Answer explanation

This is a 45°-45°-90° Triangle, so y = 5.

Triangle MNP and JKL are similar right triangles. Between which pairs of points are the slopes the same? Choose all that apply.

• N and P; K and J

• M and P; J and L

• M and N; K and L

• N and P; J and L

Identify the slope of the hypotenuse of triangle DEF.

• 1

• -1

• 3

• -3

Identify the slope of the hypotenuse of triangle ABC.

• 1

• -1

• 3

• -3

Triangle HJK and triangle PMK are similar right triangles. The coordinates of all the verticces are integers. Which statement is true about the slope of line HK and the slope of line PK.

• The slope of line HK is less than the slope of line PK because the ratio of the change in y-values of the endpoints to the change in x-values of the endpoints is less for line HK than it is for line PK.

• The slope of line HK is equal to the slope of line PK because the ratio of the change in y-values of the endpoints to the change in x-values of the endpoints is the same for line HK as it is for line PK.

• The slope of line HK is greater than the slope of line PK because the ratio of the change in y-values of the endpoints to the change in x-values of the endpoints is greater for line HK than it is for line PK.

• The relationship between the slope of line HK and the slope of line PK cannot be determined because the traingles are congruent.

Identify the slope (CA) of triangle ABC.

• 1/3

• 3

• -3

• -1/3

Triangles ABC and DEF are similar. The slope of triangle ABC is...

• which is the same as the slope of triangle DEF.

• 3/4 which is the slope of hypotenuse of triangle DEF.

• 4/3 which is the slope of triangle DEF.

• -1 which is the same as the slope of triangle DEF.

• 2/3

• 3/4

• 3/2

• 1/3