What is the slope and intercept for y=9?

Question

Vedantu Content Team · Accepted Answer

Hint: We need to find the slope and intercept of the line y=9. We start to solve the given question by plotting the graph of the line y=9. Then, we find the slope of the given line using the slope formula given by $\dfrac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}}$ to get the desired result.Complete step-by-step solution:We are given a line equation and are asked to find the slope of the given line equation. We will be solving the given question using the slope formula $\dfrac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}}$ .The slope of a straight line is used to determine the steepness of the line. It is usually the ratio of the amount y increases to the amount x increases.The slope of the line is usually denoted by a variable m.It is given as follows,$\Rightarrow m=\dfrac{{{y}_{2}}-{{y}_{1}}}{{{x}_{2}}-{{x}_{1}}}$Here,$\left( {{x}_{1}},{{y}_{1}} \right),\left( {{x}_{2}},{{y}_{2}} \right)$ are the first and second coordinates in the line.According to the question,We need to find the slope of the line y=9.The graph of the line y=9 is represented as follows,

From the graph,We observe that the line y=9 does not pass through the horizontal axis or the x-axis.From the above, The value of y is always equal to 9 for any values of the horizontal coordinates.Following the same, we get,${{y}_{2}}=9$${{y}_{1}}=9$${{x}_{1}}={{x}_{1}}$${{x}_{2}}={{x}_{2}}$Substituting the above values of coordinates in the slope formula, we get,$\Rightarrow m=\dfrac{\left( 9-9 \right)}{{{x}_{2}}-{{x}_{1}}}$Simplifying the above equation, we get,$\Rightarrow m=\dfrac{0}{{{x}_{2}}-{{x}_{1}}}$$\therefore m=0$The slope of the line y=9 is zero.The y-intercept is the point where the graph of the function crosses the y-axis. The point lies on the y-axis. Hence, the coordinates of the y-intercept are given by $\left( x,y \right)$ where the value of $x=0$According to our question,We need to find the value of the y-intercept of the line $\Rightarrow y=9$From the graph, we know that the graph of the line is crossing the y-axis at the point $A\left( 0,9 \right)$ .So, the coordinates of the y-intercept are given by $\left( 0,9 \right)$ $\therefore $ The slope of the line y=9 is zero and the intercept is at a point $\left( 0,9 \right)$Note: The slope of the line can be alternatively found as follows,The general equation of the straight line is given by $y=mx+c$Here,m = slopeRepresenting the line y=9 in the form of y=mx+c, we get,$\Rightarrow y=0x+9$$\therefore y=0x+9$Comparing the above equation with the standard line equation, the slope of the line y=9 is zero.