Write an equation of the line containing the specified point and parallel to the indicated line.(1,4)3x+y=5
thanks for the help Damon
To find the equation of a line parallel to the given line, we need to determine the slope of the given line first. The equation of a line in slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.
Step 1: Convert the given equation to slope-intercept form.
3x + y = 5
y = -3x + 5
Step 2: Since the line we are looking for is parallel, it will have the same slope as the given line. The slope of the given line is -3.
Step 3: Use the point-slope form of the equation y - y1 = m(x - x1), where (x1, y1) is the given point and m is the slope determined in step 2.
(x1, y1) = (1, 4) and m = -3.
y - 4 = -3(x - 1)
Step 4: Simplify the equation.
y - 4 = -3x + 3
y = -3x + 7
Therefore, the equation of the line containing the point (1, 4) and parallel to the line 3x + y = 5 is y = -3x + 7.
To find the equation of a line parallel to another line, we need to ensure that both lines have the same slope. Recall that the slope-intercept form of a linear equation is given by y = mx + b, where m is the slope of the line.
First, let's find the slope of the given line 3x + y = 5. To determine the slope, we need to rewrite the given equation in the slope-intercept form:
y = -3x + 5
Comparing this equation with the slope-intercept form, we can see that the slope (m) is -3.
Since the line we want to find is parallel to the given line, it will have the same slope of -3.
Now that we have the slope (-3) and a point (1,4) that the line passes through, we can use the point-slope form of a linear equation to find the equation of the line:
y - y₁ = m(x - x₁)
Substituting the values, we have:
y - 4 = -3(x - 1)
Expanding the equation:
y - 4 = -3x + 3
Finally, rearranging the equation to the standard form:
3x + y = 7
Therefore, the equation of the line containing the point (1,4) and parallel to the line 3x + y = 5 is 3x + y = 7.
original line is
y = -3 x + 5
the slope is thus -3
and any line parallel is of form
y = -3 x + b
all we need is b
4 = -3(1) + b
b = 7
so
y = -3 x + 7