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Write an equation in slope-intercept form for the line that passes through the given point and is parallel to the graph of the given equation. (-2,3), y = -3/4x + 4

User Itpetersen
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Final answer:

To write a slope-intercept form equation for a line parallel to y = -3/4x + 4 that passes through (-2,3), we use the same slope of -3/4. Substituting the point into the slope-intercept form and solving for the y-intercept gives us the new equation: y = -3/4x + 3/2.

Step-by-step explanation:

The student asked to write an equation in slope-intercept form for a line that is parallel to the given equation y = -3/4x + 4 and passes through the point (-2,3). To find the equation of a line that is parallel to another, we need to use the same slope because parallel lines have the same slope. The slope mentioned in the provided equation is -3/4, hence the new line will also have this slope.

Now, using the point (-2,3) and the slope -3/4, we can use the slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept, to find the new y-intercept. Plugging in the coordinates of the point and the slope:

y = -3/4x + b
3 = (-3/4)(-2) + b
3 = 3/2 + b
b = 3 - 3/2
b = 3/2

Finally, our new equation is:

y = -3/4x + 3/2

This new line will be parallel to the given line and pass through the specified point.

User Cvetelina
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4 votes

The equation in slope-intercept form for the line that passes through (-2,3) and is parallel to the given equation is y = -3/4x + 3/2.

To find an equation in slope-intercept form for a line parallel to the given equation, we need to keep the same slope and find a different y-intercept. The given equation is y = -3/4x + 4 and the point the line passes through is (-2,3).

The slope-intercept form of an equation is y = mx + b, where m represents the slope and b represents the y-intercept.

In the given equation, the slope is -3/4, so the parallel line will also have a slope of -3/4. Plugging in the coordinates of the given point (-2,3), we can substitute -3/4 for m and solve for b:

3 = (-3/4)(-2) + b

3 = 3/2 + b

b = 3 - 3/2

b = 6/2 - 3/2

b = 3/2

Thus, the required equation for the given line in slope-intercept form is y = -3/4x + 3/2.

Write an equation in slope-intercept form for the line that passes through the given-example-1
User Do Will
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