Questions: Graph the line with slope 3 passing through the point (-3,-5).

Graph the line with slope 3 passing through the point (-3,-5).
Transcript text: Graph the line with slope 3 passing through the point $(-3,-5)$.
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Solution

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Solution Steps

Step 1: Given a point and slope

Given a point (x1,y1)=(3,5)(x_1, y_1) = (-3, -5) and a slope m=3m = 3.

Step 2: Use the point-slope form to find the y-intercept

The point-slope form of a line equation is yy1=m(xx1)y - y_1 = m(x - x_1). Substituting the given values, we get y+5=3(x+3)y + 5 = 3(x + 3). Rearranging to slope-intercept form y=mx+by = mx + b, we find the y-intercept bb. b=y1mx1=533=4b = y_1 - m\cdot x_1 = -5 - 3\cdot-3 = 4.

Step 3: Graphing the line

With the slope m=3m = 3 and the y-intercept b=4b = 4, the equation of the line is y=3x+4y = 3x + 4. To graph the line, plot the y-intercept on the y-axis. Then, use the slope to find another point on the line. Draw a straight line through these points to complete the graph.

Final Answer: The equation of the line is y=3x+4y = 3x + 4.

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