Question
1)) The equation for line t can be written as y+8=(1)/(2)(x+7) Line u includes the point (8,10) and is parallel to line t. What is the equation of line u?
Solution
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Resposta
To find the equation of line u, we need to use the point-slope form of a linear equation, which is given by:
where
is a point on the line and
is the slope of the line.Since line u is parallel to line t, it will have the same slope as line t. The slope of line t can be found by rearranging the equation
into slope-intercept form (
), where
is the slope.Rearranging the equation, we get:
Simplifying further, we have:
From this equation, we can see that the slope of line t is
.Now, we can use the point-slope form to find the equation of line u. We know that line u passes through the point
, so we can substitute these values into the point-slope form:
Simplifying this equation, we get:
Finally, rearranging the equation to slope-intercept form, we have:
Therefore, the equation of line u is
.