Question

How do you write an equation of a line parallel to y = 4x + 2, y – intercept at 4?

Answer 1

Hint: We are asked to find the line parallel to y = 4x + 2 and having y – intercept at 4. To find the line, we will learn about the form of lines, then we will find how the slope of the parallel lines is connected. After that we will use y = 4x + 2 to find the slope of our required line. Once, we have the slope and intercept, we will form our required equation.

Complete step-by-step solution:
We are asked to find the equation of a line that is parallel to the line given as y = 4x + 2 and whose y – intercept is 4. To answer this we should know what the equation of a line is. We know the standard form of the equation of the line is given as ax + by + c = 0 where a, b and c are integral. We also write the equation in some other form like a point – slope form or slope-intercept form, etc.
Now, as in our equation, we have mentioned about y – intercept then we will also understand how in slope-intercept form is given. The equation of the line of the form y = mx + c is called the slope intercept form of the line where m denotes the slope and c denotes the y – intercept.
Now, we are given that our required line is parallel to the line y = 4x + 2. To find the equation of our line, we will use the slope intercept form as we are given the intercept (y – intercept) to us as 4.
Now, firstly, we will try to find the slope of our line. Remember that whenever two lines are parallel, then their slopes are equal as we are given that our required line is parallel to y = 4x + 2. This means that the slope of our line is the same as the slope of the line y = 4x + 2.
Now, we can compare the given line y = 4x + 2 to the slope intercept form y = mx + c. We can see that the value of the slope m is 4. So, the slope of the line is 4. This means that the slope of our line is also 4. So, m = 4 and we are also given that the value of y – intercept is 4, this means we have y – intercept c = 4. So, using m = 4 and c = 4 in slope intercept form y = mx + c.
We get the slope intercept form of our line as y = 4x + 4. Hence, our line equation is y = 4x + 4 or we can convert it into ax + by + c = 0 which is the standard form. Therefore, we will get the equation of our line as – 4x + y – 4 = 0.

Note: While we solve the equation, we should be careful on solving the terms that include brackets, when we have the term inside the bracket and we have to multiply that with some term. Error happens like a(b + c) = ab + c, we may miss calculating the product with each term. Also, y – intercept is defined as the point on the y – axis where the given line cuts the y – axis, y – intercept is 4 means the line cuts the y – axis at 4.