6x+5y=17 find the equation, in slope-intercept form, for the line which is parellel to this line and passes through the point (-10,3)
6x+5y = 17. P(-10,3).
m1 = m2 = -A/B = -6/5.
(-10,3).
Y = mx+b = 3.
(-6/5)*(-10) + b = 3
12+b = 3
b = 3-12 = -9.
Eq: Y = (-6/5)x-9.
To find the equation of a line parallel to the given line and passing through the point (-10, 3), we need to determine the slope of the given line first. The slope-intercept form of a line is given by y = mx + b, where m represents the slope of the line.
Given: 6x + 5y = 17
We can rearrange this equation to solve for y in terms of x:
5y = -6x + 17
y = (-6/5)x + 17/5
From this equation, we can see that the slope of the given line is -6/5.
Parallel lines have the same slope. So, the slope of the line we want to find will also be -6/5.
Now, using the point-slope form of a linear equation, we can write the equation of the line passing through (-10, 3) using the slope -6/5:
y - y1 = m(x - x1)
Substituting the values of the point (-10, 3) and the slope -6/5:
y - 3 = (-6/5)(x - (-10))
Simplifying:
y - 3 = (-6/5)(x + 10)
y - 3 = (-6/5)x - 12
y = (-6/5)x - 12 + 3
y = (-6/5)x - 9
So, the equation of the line parallel to the given line and passing through the point (-10, 3) is y = (-6/5)x - 9.
To find the equation in slope-intercept form for the line parallel to 6x + 5y = 17 and passing through the point (-10, 3), we need to follow these steps:
Step 1: Determine the slope of the given line.
Step 2: Use the slope to find the slope of the parallel line.
Step 3: Use the slope-intercept form (y = mx + b) and substitute the known values to find the y-intercept (b).
Step 4: Write the final equation using the found slope and y-intercept.
Let's begin step by step:
Step 1: Determine the slope of the given line.
The given line is 6x + 5y = 17. To find the slope, we need to put the equation in slope-intercept form, which is y = mx + b, where 'm' represents the slope.
Let's rearrange the equation to solve for y:
5y = -6x + 17
Divide both sides by 5:
y = (-6/5)x + 17/5
From this equation, we can determine that the slope of the given line is -6/5.
Step 2: Use the slope to find the slope of the parallel line.
Since the parallel line has the same slope as the given line (-6/5), the slope of the parallel line is also -6/5.
Step 3: Use the slope-intercept form (y = mx + b) and substitute the known values to find the y-intercept (b).
We have the formula y = mx + b. We know the slope (m = -6/5) and a point on the line (-10, 3). We can substitute these values into the formula to solve for the y-intercept (b):
3 = (-6/5)(-10) + b
3 = 12 + b
b = 3 - 12
b = -9
Step 4: Write the final equation using the found slope and y-intercept.
Using the slope-intercept form (y = mx + b) and inserting the values we found:
The equation of the line parallel to 6x + 5y = 17 and passing through the point (-10, 3) is:
y = (-6/5)x - 9