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yuradex [85]
2 years ago
6

Graph the line with slope -1/2 passing through the point (-1,-2)

Mathematics
1 answer:
Bezzdna [24]2 years ago
6 0

Answer:

See attachment for graph

Step-by-step explanation:

Given

m = -\frac{1}{2}

(x_1,y_1) = (-1,2)

Required

Graph the line

First, is to determine the equation of the line using:

m = \frac{y - y_1}{x - x_1}

So:

-\frac{1}{2} = \frac{y - 2}{x - -1}

-\frac{1}{2} = \frac{y - 2}{x +1}

\frac{-1}{2} = \frac{y - 2}{x +1}

Cross multiply:

(y -2) * 2 = -1 * (x + 1)

(y -2) * 2 = -x -1

Solve for y - 2

y -2 = -\frac{x}{2} -\frac{1}{2}

Solve for y

y  = -\frac{x}{2} -\frac{1}{2} + 2

y  = -\frac{x}{2} +\frac{-1+4}{2}

y  = -\frac{x}{2} +\frac{3}{2}

<em>The above equation will then be plotted on the graph (See attachment)</em>

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Algebra 2 Math question Grade 11
Paha777 [63]

Answer:

\displaystyle y=\frac{4}{5}x+\frac{13}{5}

Step-by-step explanation:

The equation of the line in slope-intercept form is:

y=mx+b

Where m the slope of the line and b the y-intercept.

When two points are given, it's convenient to calculate the slope first.

Suppose we know the line passes through points A(x1,y1) and B(x2,y2). The slope can be calculated with the equation:

\displaystyle m=\frac{y_2-y_1}{x_2-x_1}

The points are (3,5) and (-2,1):

\displaystyle m=\frac{1-5}{-2-3}=\frac{4}{5}

The equation is now:

\displaystyle y=\frac{4}{5}x+b

To calculate b, we use any of the given points and solve for b. Use (3,5):

\displaystyle 5=\frac{4}{5}3+b

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Solve:

\displaystyle b=5-\frac{12}{5}=\frac{13}{5}

The required equation of the line is:

\boxed{\displaystyle y=\frac{4}{5}x+\frac{13}{5}}

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