How do you write an equation of the line that passer through points (0, 7) and (1, 10)?

Question

Avery Alexander · Accepted Answer

Rhis line has equation #y=3x+7#. See explanation.

A general equation of a linear function can be written as #y=ax+b# Since one of the given points is the function's Y-intercept we can write that #b=7#. Now we have to ind a value of #a# for which #(1,10)# belongs to the graph. If we substitute the given values we get: #10=a+7# #a=3# So finally the function is #y=3x+7#

Eva Adamson · Answer

undefined You can write the equation of the line passing through the points (0, 7) and (1, 10) using the point-slope form:

y - y₁ = m(x - x₁)

where:
- (x₁, y₁) are the coordinates of one point (0, 7),
- (x, y) are the coordinates of any point on the line,
- m is the slope of the line.

First, find the slope using the formula:

m = (y₂ - y₁) / (x₂ - x₁)

Plugging in the coordinates (0, 7) and (1, 10):

m = (10 - 7) / (1 - 0) = 3

Now, using the point-slope form with one of the points:

y - 7 = 3(x - 0)

Simplify:

y - 7 = 3x

So, the equation of the line passing through the points (0, 7) and (1, 10) is:

y = 3x + 7