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This is the second of our many quizzes on x-intercepts and y-intercepts. Click on this to access more such competitive quizzes on intercepts on a straight line.

X-intercepts and Y-intercepts Quiz 2

mathematics

 Find the equation of a line $m$ given in the following graph?<img  src="https://cmds-vedantu.s3.ap-southeast-1.amazonaws.com/prod/question-sets/500dcce3-d81b-4698-aaef-a3da576335573835581502004787457.png"/>

 Find the coordinates of $A$ and $B$ and then use intercept form to get the required answer.

  $\text{From the given graph, we get:} \\ \text{Coordinates of }A = (0, 6 – 2) = (0, 4) \\ \text{Coordinates of }B = (6 – 2, 0) = (4, 0) \\ \text{Using intercept form, equation of line “m” is,} \\ \dfrac{x}{a}+\dfrac{y}{b}=1 \\ \Rightarrow \dfrac{x}{4}+\dfrac{y}{4}=1 \\ \Rightarrow x+y=4 \\ $  

 Which of the following is a y-intercept of that line which intersects perpendicularly to the line $28x+21y-6=0$ at point $(3, -7)$. 

 First find slope $m$ and then slope $n$. Now, find the equation using point-slope form.

  $\text{Slope-intercept form i.e., }y = mx + c\text{ of }28x+21y-6=0 \text{ is} \\ y=\dfrac{-4}{3}x+\dfrac{2}{7}\\\Rightarrow m=\dfrac{-4}{3}. \\ \text{Since, the required line is perpendicular to the given line.} \\ \Rightarrow m\times n=-1\Rightarrow n=\dfrac{3}{4},\text{ where “n” is the slope of a required line.} \\ \text{Since the required line is passing through (3, -7).} \\ \text{So, using point-slope form i.e., } y-{{y}_{1}}=n(x-{{x}_{1}}) \\ \text{By putting y = 0, we get:} \\ \Rightarrow y+7=\dfrac{3}{4}(x-3) \\ \Rightarrow 28=3x-9\Rightarrow x=\dfrac{37}{3} \\ $ 

 Given that $J = 100$ when $M = 65$ and $M = 80$ when $J = 150$. Assuming the linear relation between $J$ and $M$, find the value of $M$ when $J = 0$? 

 Use two-point form to find the equation and then put $J = 0$.

 $\text{Suppose “J” is along X-axis and “M” is along Y-axis.} \\ \text{Then we have (100, 65) and (150, 80) points in “XY” plane.} \\ \text{So, by two-point form we have:} \\ \Rightarrow M-65=\dfrac{80-65}{150-100}(J-100) \\ \Rightarrow M-65=3\times (-10)\text{    (put J}=0\text{)} \\ \Rightarrow M=35 \\ $ 

 What will be the equation of a line if sum and difference of its slope and y-intercept are given as $\dfrac{-9}{7}$ and $\dfrac{13}{7}$ respectively. Assume $c < m$ in $y = mx + c$.

 Find the value of $m$ and $c$ using the given relations and then find the equation using slope-intercept form.

 $\text{The required equation of a line is y=mx+c} \\ \text{W.K.T “c” is a y-intercept. So,  we have:} \\ \Rightarrow m+c=\dfrac{-9}{7}\text{ and }m-c=\dfrac{13}{7}\text{ } \\ \Rightarrow m=\dfrac{2}{7}\text{ and }c=\dfrac{-11}{7} \\ \therefore \text{ Required equation}\\ \Rightarrow y=\dfrac{2}{7}x-\dfrac{11}{7} \\ \Rightarrow 2x-7y-11=0 \\ $ 

 Given that the product of $x$ and $y-$intercepts of a line is 36. If x-intercept is negative then find the equation of a line whose y-intercept is four times the value of x-intercept.

 Find the equation in intercept form and then find the value of a using the given condition.

 $\text{Let x-intercept = a. Then, y-intercept =4a}\\ \text{Equation of a line in intercept form is} \\ \Rightarrow \dfrac{x}{a}+\dfrac{y}{4a}=1 \\ \Rightarrow 4x+y=4a \\ \text{Also, we have} \\ a\times 4a=36 \\ \Rightarrow a=\pm 3\Rightarrow a=-3\text{        }(\because x\text{-intercept}=a<0) \\ \therefore \text{ Required equation }4x+y+12=0$