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Diano4ka-milaya [45]
3 years ago
6

Line "m" has intercepts (7,0) and (0, -2)

Mathematics
1 answer:
givi [52]3 years ago
6 0
The equation of a line is usually written in what's called <em>slope-intercept form</em>.

Slope-intercept form is written as y = mx + b where m = slope and b = the y-intercept.

The slope of a line can easily be found just by using two points on the line. The slope is equal to the rise over the run, or the difference in y over the difference in x, between the two points.

slope = \frac{y_2-y_1}{x_2-x_1} = \frac{-2-0}{0-7} = \frac{-2}{-7} = \boxed{\frac{2}{7}=m}

The y-intercept of the line is the point at which it intersects the y-axis. (The vertical axis.) All points on the y-axis have an x coordinate of 0, so we would then add or subtract the rise and run to a point on the line until we reached x = 0.

Fortunately, we already have this point! It's (0, -2)!

y-intercept=\boxed{-2=b}

Now we just need to put our slope and y-intercept into the equation.

\boxed{\boxed{y=\frac{2}{7}x-2}}

And to test if a point is on this line, just plug in the x and y coordinates and see if the equation is true!

-16 = \frac{2}{7}*49-2 \\ -16 = 14 - 2 \\ -16  \neq 12,\ \therefore line\ m\ does\ not\ contain\ (49, -16)
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A line with a slope of 1 passes through the points (5,w) and (-7,-9). what is the value of w?
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