A line passes through the points (0, 2) and (2, 10). What is its equation in slope-intercept form?

Mathematics

2 answers:

levacccp [35]3 years ago

6 0

Answer:

y = 4x + 2

Step-by-step explanation:

The slope-intercept form:

y = mx + b, where m is the slope, b is the y-intercept

Find the slope using given points:

m = (10 - 2)/(2 - 0) = 8 / 2 = 4

The y-intercept is given with point (0, 2):

b = 2

The line is:

y = 4x + 2

Alex Ar [27]3 years ago

6 0

(0,2)
(2,10)

$\\ \sf{:}\Rrightarrow m=\dfrac{10-2}{2-0}=\dfrac{8}{2}=4$

Put in slope intercept form

$\\ \sf{:}\Rrightarrow y=mx+b$

$\\ \sf{:}\Rrightarrow 2=4(0)+b$

$\\ \sf{:}\Rrightarrow 2=b$

Equation of the line

$\\ \sf{:}\Rrightarrow y=4x+2$

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Allison claims that the (triangle)ABQ is similar to (triangle)RPQ, given that AB and PR are parallel. Which of Allison's claims

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I draw the two triangles, see the picture attached.

As you can see, angle 1 and 2 are vertically opposite angles because they are formed by the same two crossing lines and they face each other.

Angles ABQ and QPR, as well as angles BAQ and QRP, are alternate interior angles because they are formed by two parallel lines crossed by a transversal, and they are inside the two lines on opposite sides of the transversal.

Hence, Allison's correct claims are:
1 = 2 because they are vertically opposite angles.
BAQ = QRP because they are alternate interior angles.

Therefore Allison, in order to prove her claim, can use the AA similarity theorem: if two angles of a triangle are congruent to two angles of the other triangle, then the two triangles are similar.