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aev [14]
3 years ago
10

Graphing in Point-Slope Form y−y1=m(x−x1) ​ Graph the equation y+7=−45(x−4) ?

Mathematics
1 answer:
nevsk [136]3 years ago
3 0

Answer:

<h2>The graph is in the attachment.</h2>

Step-by-step explanation:

The point-slope form of an equation of a line:

y-y_1=m(x-x_1)

<em>m</em><em> - slope</em>

<em>(x₁, y₁)</em><em> - a point on a line</em>

The slope-intercept form of an equation of a line:

y=mx+b

<em>m</em><em> - slope</em>

<em>b</em><em> - y-intercept → (0, b)</em>

We have the equation in a point-slope form:

y+7=-\dfrac{4}{5}(x-4)

y-(-7)=-\dfrac{4}{5}(x-4)

Therefore we have one point: <em>(4, -7)</em><em>.</em>

<em>Convert to the slope-intercept form:</em>

y+7=-\dfrac{4}{5}(x-4)              <em>use the distributive property</em>

y+7=-\dfrac{4}{5}x+\left(-\dfrac{4}{5}\right)(-4)

y+7=-\dfrac{4}{5}x+\dfrac{16}{5}

y+7=-\dfrac{4}{5}x+3\dfrac{1}{5}          <em>subtract 7 from both sides</em>

y=-\dfrac{4}{5}x-3\dfrac{4}{5}

Put <em>x = -1</em><em> </em>to the equation:

y=-\dfrac{4}{5}(-1)-3\dfrac{4}{5}=\dfrac{4}{5}-3\dfrac{4}{5}=-3

Therefore we have the second point <em>(-1, -3)</em>.

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