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sattari [20]
3 years ago
13

A line passes through the point (2, 10) and has a y-intercept of 4. What is the equation of the line?

Mathematics
1 answer:
KatRina [158]3 years ago
3 0

Answer:

y=3x+4

Step-by-step explanation:

Hi there!

<u>What we need to know:</u>

  • Linear equations are typically organized in slope-intercept form: y=mx+b where m is the slope and b is the y-intercept (the value of y when x is equal to 0)

<u>1) Determine the slope (m)</u>

m=\frac{y_2-y_1}{x_2-x_1} where two points that the line passes through are (x_1,y_1) and (x_2,y_2)

We're given the point (2,10) and the y-intercept of 4. Recall that the y-intercept occurs when x is equal to 0. This means that the y-intercept occurs at (0,4), giving us our second point.

Plug these points into the equation

=\frac{10-4}{2-0}\\=\frac{6}{2}\\=3

Therefore, the slope of the line is 3. Plug this into y=mx+b

y=3x+b

<u>2) Determine the y-intercept (b)</u>

The y-intercept is given; it is 4. Plug this back into y=3x+b

y=3x+4

I hope this helps!

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