Please help step by step.
What is the slope of a line that is parallel to the line with the equation 2y + 4 + 3x?
Write an equation in standard form of the line that passes through (1, -2) and is parallel to the line -5x + y = 9.
The equation of the line that passes through (1, -2) and is parallel to the line 2y + 4 + 3x is:
-5x + y = -13
Sure! I'd be happy to help you step by step.
1. To find the slope of a line parallel to a given line, you need to know that parallel lines have the same slope. So, the first step is to determine the slope of the given line.
2. The equation of the given line is 2y + 4 + 3x. However, there seems to be a missing equal sign. Assuming that the equation should be 2y + 4 = 3x, let's proceed with that.
3. To find the slope of this line, we will rewrite the equation in slope-intercept form, which is y = mx + b, where m represents the slope.
4. Rearranging the equation, we get 2y = 3x - 4.
5. Divide both sides of the equation by 2 to isolate y: y = (3/2)x - 2.
6. Now we can see that the slope of the given line is 3/2. Therefore, any line parallel to it will also have a slope of 3/2.
-----
Now let's move on to the second question about writing an equation in standard form.
1. The standard form of a linear equation is given by Ax + By = C, where A, B, and C are real numbers.
2. We are given the condition that the line we need to find is parallel to the line -5x + y = 9 and passes through the point (1, -2).
3. First, let's determine the slope of the given line. Rewrite the equation in slope-intercept form: y = 5x + 9.
4. Comparing this equation with the slope-intercept form (y = mx + b), we can see that the slope of this line is 5.
5. Since we want to find a line parallel, which means it has the same slope, we can use the slope of 5 for the new line.
6. Now, let's use the point-slope form of a linear equation: y - y1 = m(x - x1), where (x1, y1) represents the coordinates of a point on the line.
7. Plugging in the values from the point (1, -2), we have y - (-2) = 5(x - 1).
8. Simplifying, we get y + 2 = 5x - 5.
9. Rearranging the equation, we get 5x - y = 7.
10. The equation in standard form is now 5x - y = 7.
I hope these step-by-step explanations were helpful! Let me know if you have any further questions.
To find the slope of a line that is parallel to the line with the equation 2y + 4 + 3x, we need to determine the slope of the given line.
The given equation is in the form of y = mx + b, where m represents the slope.
2y + 4 + 3x = 0
Rearranging the equation to isolate y:
2y = -3x - 4
y = -3/2x - 2
We can see that the slope of the line is -3/2.
To write an equation in standard form that passes through the point (1, -2) and is parallel to the line -5x + y = 9, we can use the slope-intercept form of a line: y = mx + b.
First, let's determine the slope of the given line -5x + y = 9.
Rearrange the equation to isolate y:
y = 5x + 9
We can see that the slope of the line is 5.
Since we want to find a line parallel to this line, the new line will have the same slope.
Using the point-slope form of a line, we have:
y - y1 = m(x - x1)
Substituting the given point (1, -2) and the slope (5) into the equation, we get:
y - (-2) = 5(x - 1)
y + 2 = 5x - 5
y = 5x - 7
To write the equation in standard form, rearrange the equation:
-5x + y = -7
So, the equation in standard form that passes through (1, -2) and is parallel to the line -5x + y = 9 is -5x + y = -7.